Prisms and Pyramids

I need help with a lot of these math problems. Not sure exactly how to get them. Just want help understanding how to get the answer:

For 1 through 10, what is the area and volume of the given shape, if the length of one side of the base is 6, the height is 8, and the slant height is 10? (Not all shapes will require all three numbers.)

Re: Prisms and Pyramids

It seems you get two equations with two variables.One equation for the lateral area has two variables, say x and y.One equation for the volume is another equation with x and y.

5. the base is an isosceles triangle with a height of 8 and a base of 3 (sides of 6)I'm a little unclear with this.

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Re: Prisms and Pyramids

Ok, from the link I understood how to get the area. So the base they give me is 6 as the base and the height is 8. So i have done:A = .50 x 6 x 8 = 24

So now I have the area, I times it with height to get: V = 24 x 8 = 192Now I'm not sure if I'm doing it EXACTLY right. I'm trying to figure out the answer for #1. To me it seems as if I got the lateral area which I feel is wrong:The shape is a right prism with:

Re: Prisms and Pyramids

hi demha,

The height = 8 measurement cannot be for the triangle because it is equilateral with side = 6. There isn't enough space inside it for a height of 8. You can get it's height by using your earlier work on trig etc.

The 8 must refer to the height of the prism. Stand it on its triangular base and it is 8 high.

In my diagram I cannot make the triangle look equilateral that way round so I've shown it with the triangle as the front and then the 8 becomes its length.

So work out the height of the triangle, then its area, then the volume.

The rectangular sides are easy as they are all the same length and width.

Looking at those answers, I think the 'lateral' area may mean just the rectangles, not the triangular ends.

Bob

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Re: Prisms and Pyramids

I've done some further researching and I think I am understanding it more now. First I need to get the area of the triangle shape. I believe that would be:6 x 3 = 18.Now:V = A x HV = 18 x 8 | v = 288Is that correct?

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Volume:H = 3 x 6 This is the area of the end rectangle (18). Pythagoras and square roots are unnecessary as you have the area at this point.H = 18H = sqrt {6 x 3}H = 6 {sqrt 3}

A = 1/2 x 6 x 6 {sqrt 3}A = 18 {sqrt 3}

V = 18 {sqrt 3} x 8= 144 {sqrt 3}

Lateral Area:

The sides of the prism are (i) a rectangle 6 by 8 (ii) a rectangle 3 by 8 (iii) another rectangle 6 by 8 and finally (iv) another rectangle 3 by 8. What you have worked out here is not correctly the way to get the lateral area.

Would I be using the same method as #1 to get the volume & lateral area for this?

Yes, that's right. And you diagram looks good to me too.

Sorry if it's so huge I'm trying to figure out how to work this image upload thing

Well the image upload worked so that's ok. You could have cropped some white space to save on the image size. If you're using Paint you can move the right and bottom borders in, then rotate the image 180 and shrink the other two borders.

Bob

Children are not defined by school ...........The FonzYou cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Re: Prisms and Pyramids

Look back to your diagram. The triangle has sides 6,6 and 3. Make a right angle by finding the midpoint of the base. The right angled triangle has sides of 6, 1.5 and h, where h is the height of the triangle.

Then half base x h and finally x by 8.

The lateral area isn't correct either because only one of the lateral rectangles is 3 by 8.

Bob

Children are not defined by school ...........The FonzYou cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei